One of the ways to increase the concentrating ability of solar concentrators used for pumping of lasers is an additional
concentration of a sunlight by a secondary concentrator allocated in a focal area of the primary concentrator. Limiting
concentrations of those compound systems on the basis of non-imaging optics have been received by Winston. However
more detailed calculations on the basis of irradiance integral are necessary for designing and practical realization of such
systems. It is especially important for the systems including generally compound of two secondary concentrators. The
full design procedure for concentration by systems of type compound parabolic concentrator or Winston concentrator
(focon) and a cone concentrator is developed in the work in view of real distribution of brightness on a solar disk and
discrepancies of primary concentrator geometry. The generalized dependences of efficiency of compound systems for
the maximal and mean concentration in a focal plane of the primary paraboloidal concentrator depending on its
disclosing angle U0 and discrepancies of geometry are received.
It is shown, that focon only up to U0 < 30° is more effective, than the cone and further their efficiencies are identical. It is
shown, that secondary concentrator allows to increase the pumping efficiency not less, than 30%.